Interior and Exterior Polygon Angles

The sum of the interior angles of a polygon with n sides is given by the formula: $$(n - 2) \times 180^\text{°}$$ .

To find the measure of one interior angle of a regular polygon with n sides, use the formula: $$\frac{(n - 2) \times 180^\text{°}}{n}$$ .

The measure of one exterior angle of a regular polygon with n sides is given by the formula: $$\frac{360^\text{°}}{n}$$ .

The sum of the exterior angles of any polygon is always $$360^\text{°}$$ .

To find the number of sides (n), use the formula: $$n = \frac{(1080^\text{°} + 360^\text{°})}{180^\text{°}} = 8$$ . Thus, it is an octagon.

The measure of one interior angle of a regular hexagon is $$120^\text{°}$$ .

To find the number of sides (n), use the formula: $$n = \frac{(135^\text{°} \times n) - 360^\text{°}}{180^\text{°}}$$ . Solving gives n = 8, so it is an octagon.

The interior and exterior angles of a polygon are supplementary, meaning they add up to $$180^\text{°}$$ .

The sum of the interior angles of a 24-gon is $$(24 - 2) \times 180^\text{°} = 3960^\text{°}$$ .

The measure of one exterior angle in a regular hexagon is $$60^\text{°}$$ .